Turn in #5 is due Tuesday, Nov. 1, 2016!
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For #1, how do we determine the radius of the original circle?
ReplyDelete- Xan
It is arbitrary and irrelevant.
DeleteFor 1c, should there be two angles/answers that Sally can use to maximize the volume?
ReplyDeleteWell, yes since if theta is the angle removed then 360-theta is what is left over...
DeleteFor 3a, should Lopitals rule be used to prove the answer?
ReplyDeleteYou don't need L'hopital's rule to get the answer you just need to change the way the function is written when solving for the limit to make the answer clearer.
DeleteAlthough you do not need L 'Hopital's rule to get the answer, it does help. Once you prove that you can use it, you can simplify the numerator and denominator through derivation, which makes it easier to find the limit.
Delete- Andrew Saad
on 1b), is the angle we are looking for the one that she removes from the part removed in 1a) ?
ReplyDeleteEstelle
Yes
DeleteThis comment has been removed by the author.
ReplyDeleteon page 205 #44, does f have an inflection point at x=c?
ReplyDeleteon pg. 192 #48 how do you show that the equation has exactly one solution to the interval its on?
ReplyDeleteIVT, MVT, show f doesn't change directions, etc....many ways
DeleteIf f' has a cusp or sharp point, is that a point of inflection?
ReplyDeleteChance Stephenson
Not 100% sure, but I believe that it would because that would mean that the f'' is changing signs at that point (definition of something being a POI) regardless of whether it's differentiable or not.
Delete-Jacob Edelson
As Jacob points out, you MUST show f" changes signs
DeleteFor #2 on the turn-in... at x=1 is the graph supposed to be sharp there (i.e. not differentiable) or is that curvy enough?
ReplyDelete-Jacob Edelson
It is sharp at x=1
DeleteFor #1 on the turn in, how do I relate theta, r, and h?
ReplyDelete-JP
This is the essence of the problem...you will need the formula for volume of a cone, Pythagoren Theorem and arc measure.
DeleteWhen would the MVT not apply to a real world problem such as the problem on page 192, #39?
ReplyDeleteEmma Lucken
I'm not sure if this is what you are asking, but I think that MVT would not apply to real world situations for problems that do not include any story element or situational elements. Example would ask if there is any point on a function where the slope reaches a certain value.
DeleteI am having trouble with 53c, can someone please give me some guidance?
ReplyDeleteIn 1a what is the equation to find arc length of the sector of the circle?
ReplyDelete- Andrew Saad
The arc length would have to do with just the radius and the angle. I don't think I can tell you the equation straight up though ;^]
Delete- Evan Gilman
On problem 1 is R the radius of the circle before the piece of paper is turned into a cone or the radius of the base of the cone?
ReplyDeleteBefore
DeleteFor problem 2e, if MVT is "works" as in the average slope is indeed a slope of the function, but the function happens to have a non differentiable point, would MVT still officially hold true?
ReplyDelete- Evan Gilman
-Evan
For MVT to apply the function must be continuous on the closed interval and differentiable on the open interval. So it's ok if it's not differentiable at the endpoint, but it must be differentiable everywhere in between.
Delete-Jacob Edelson
I'm with Charlotte... any advice on 53c?
ReplyDeleteSet the equation for the derivative of -L to 0 and find the answer for b in terms of a, or a in terms of b. Then plug this answer into the original function for -L and you should find a and b in terms of L and H. If you use these values and plug it into the original function f(-L) you should see that the equations are the same. I don't know if this made any sense but I hope it does!!
DeleteEmma Lucken